Method for filtering signal

Abstract

A method for filtering a signal. The method for filtering at least one signal to be filtered comprises the following steps, in which the filtering is determined on the basis of measurements representative of the movement of the axis of rotation:-defining at least one characterization indicator of the axis of rotation, in which the characterization indicator is obtained from a frequency analysis of the behavior of the axis of rotation (step 120); determining a filtering template according to the characterization index (step 130); and applying a filtering template to the signal to be filtered (step 140).

Description

Technical Field

[0001] The present invention relates to the characterization of a shaft rotating about an axis of rotation.

[0002] More particularly, the present invention relates to filtering indicators of gyroscopic effects and deformations of rotating shafts to facilitate control, modeling, monitoring, diagnosis and maintenance thereof. Background Art

[0003] A perfectly balanced rotating system, such as a rotating shaft, rotates about an axis of rotation such that the axis of rotation is immobile relative to its theoretical position and therefore relative to the environment in the vicinity of the axis of rotation.

[0004] However, during the rotation of the shaft, faults, deformations, gyroscopic effects or even effects due to gravity can cause the axis of rotation to move relative to its theoretical position. This is the case, for example, with deformations of the shaft due to flexible eigenmodes, which deform the shaft depending on its rotation speed.

[0005] When this defect exists, the axis of rotation is not stationary, but vibrates. It moves away from its theoretical position along a specific trajectory. More specifically, every point on the axis of rotation can move away from its theoretical position, and two points on the axis of rotation located at two different ends of the axis can have different trajectories.

[0006] The properties of a rotating shaft are usually understood through the transverse analysis of parameters. These parameters are values ​​of radial quantities, such as the position or radial velocity of the shaft, that have non-zero components in a plane orthogonal to the axis of rotation.

[0007] The changes in these quantities usually need to be characterized based on whether the shaft is rotating or not. However, many reasons can affect the rotational behavior of a rotating shaft, and it is difficult to accurately describe this behavior using reliable indicators. Summary of the invention

[0008] The object of the present invention is therefore to overcome the above-mentioned drawbacks and to propose filtering a signal to be filtered which is representative of a rotating shaft.

[0009] The object of the present invention is therefore a method for filtering at least one signal to be filtered, wherein the filtering is determined based on a measurement representative of the movement of a rotating shaft, the method comprising the following steps:

[0010] - defining at least one characterizing indicator of the rotating axis, wherein the characterizing indicator is obtained based on a frequency analysis of the rotating axis behavior;

[0011] -determine the filtering template according to the characterization index; and

[0012] - applying a filter template to the signal to be filtered, the signal to be filtered being determined based on measurements representative of the movement of the rotation axis.

[0013] This approach therefore allows the characterization indicators to become more reliable and allows the isolation of some information, which helps to understand and correct faults on rotating shafts.

[0014] Advantageously, the characterization index is obtained from the following steps:

[0015] -a) acquiring at least two input signals within a predetermined time period, said input signals comprising measurements representing movement of a rotating shaft, said measurements associated with vector quantities being non-collinear with each other and optionally coplanar with a plane intersecting the axis of rotation of the shaft;

[0016] -b) determining two components of the input signal, the components being orthogonal to each other and optionally to the axis of rotation;

[0017] -c) combining the two components into a binary signal;

[0018] -d) decomposing the binary signal time-frequency into spectral elements;

[0019] -e) determining the equivalent ellipse for each spectral element; and

[0020] -f) Extract the characterization index of the rotation axis based on the parameters of the equivalent ellipse.

[0021] Gyroscopic effects and deformations of the rotor, especially the flexible modes, are easier to consider subject to the frequency decomposition of the input signal. In fact, the rotational effects of these deformations are asynchronous, in other words, their frequencies are not directly linked to the rotation frequency of the shaft, and are therefore easier to characterize using a frequency decomposition that highlights the rotation orbits for each frequency, also called equivalent ellipses, each orbit rotating at a specific speed corresponding to the frequency considered.

[0022] This characterization of the rotating axis allows applications of control, identification, modeling, monitoring or diagnostic type.

[0023] In an embodiment, a filter template is applied to the time-frequency decomposition of the binary signal in order to obtain a filtered binary signal.

[0024] In various embodiments, the time-frequency decomposition of the binary signal to which the filter template is applied is a time-frequency decomposition obtained using a Fourier or wavelet transform, or by filtering, or using a quaternion Fourier transform.

[0025] Advantageously, the method comprises the step of obtaining the filtered input signal by projecting the filtered binary signal onto an axis collinear with the measured quantity.

[0026] In a particular embodiment, the method comprises the step of calculating a dual signal of the filtered binary signal.

[0027] In one embodiment, the at least one indicator comprises polarization rate, and / or circularity of the equivalent ellipse and / or amplitude and / or direction and / or orientation and / or synchronization indicators.

[0028] Advantageously, the filter template is defined relative to a predefined threshold value of the polarization ratio and / or a circularity indicator of the equivalent ellipse.

[0029] Advantageously, the filter template is defined based on at least one normalized index ranging between -1 and 1 or between 0 and 1.

[0030] In a particular embodiment, the filter template is a linear binary filter and / or is obtained by multiplication by a mask determined as a function of a characterization indicator and a frequency weighting.

[0031] In one embodiment, steps a) to f) are performed at least a second time for an additional plane intersecting the axis of rotation of the shaft and different from said plane, the method further comprising the step of comparing characterizing indicators of the planes.

[0032] Another object of the invention is a computer-implemented method comprising the steps of the method defined above. The method can be implemented on a real-time target, in particular in a magnetic bearing control cabinet. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a schematic diagram of the various steps of a method for obtaining an indicator according to the method of the present invention;

[0034] Figure 2 is a representation of an ellipse and its Euler parameters;

[0035] Figure 3 is Figure 1 Schematic diagram of various filtering steps applicable to the signal to be filtered after the steps. DETAILED DESCRIPTION

[0036] Figure 1 The various steps of obtaining an indicator are schematically shown, which indicator can be incorporated into the method according to the invention in a specific embodiment.

[0037] These steps allow characterizing the behavior of a rotating shaft. A rotating shaft is understood to be a shaft that rotates freely around an axis of rotation. For example, a rotating shaft is the shaft of a rotating machine.

[0038] To implement the method, firstly, step 10 of acquiring an input signal is performed.

[0039] At least two input signals are acquired within a predetermined time period, for example, the predetermined time period is a few seconds.

[0040] The input signal includes a measurement representing the motion of the rotating shaft. For example, the input signal includes a measurement of the position or velocity or acceleration or force or magnetic field or even magnetic induction of the rotating shaft. For example, the input signal is acquired using a sensor configured to measure these quantities.

[0041] In general, vector quantities are measured in terms of multiple spatially distributed components that are sensitive to the rotation of the shaft. The spatial distribution of these components is used to evaluate the motion of the rotor.

[0042] A special case is when the measurements are not collinear with each other and are coplanar with the plane that intersects the axis of rotation of the shaft. Two non-collinear measurements can be used to characterize the behavior of a rotating shaft in a plane that intersects the axis of rotation of the shaft. The additional measurement allows the characterization to be more precise.

[0043] However, measurements that are not coplanar with a plane that intersects the shaft's axis of rotation may be returned by projecting into a reference plane that intersects the shaft's axis of rotation.

[0044] For M measurements with M ≥ 2, we obtain M input signals u1(t) to u M (t), where t denotes the time at which the covering measurement was taken and the set of its values ​​is denoted by T, in other words the dates that can be assumed by t.

[0045] An intersection plane is understood to be a plane in which the measurement is performed, which plane intersects the rotation axis of the rotation shaft. The intersection plane is, for example, orthogonal to the rotation axis or not orthogonal to the rotation axis.

[0046] If the intersection plane is not orthogonal to the axis of rotation, step 20 is performed to determine two components of the input signal, wherein the components are orthogonal to each other and optionally to the axis of rotation. In other words, this step 20 is a basic variation that facilitates subsequent calculations.

[0047] In the case where the intersection plane is orthogonal to the axis of rotation, the previous steps are essentially performed.

[0048] In cases where the axis of rotation is not strictly and precisely defined, the axis is not always perfectly cylindrical and / or balanced, and / or non-deformable and / or known, the orthogonal intersecting planes are considered as study planes, which are assumed to be orthogonal to the axis of rotation, or at least sensitive to the rotational motion of the axis.

[0049] In fact, determine the two orthogonal components u x (t) and u y Step 20 of (t) is to convert the input signal u1(t) to u M (t) is achieved by averaging the projections onto two orthogonal axes x and y, which are ideally orthogonal to the axis of rotation.

[0050]

[0051] Component u x (t) and u y (t) is now in the study plane, ideally orthogonal to the axis of rotation.

[0052] Then, step 30 is performed to convert the two orthogonal components u x (t) and u y (t) into a binary signal r(t) so that the two components are combined in an equivalent way in the form of a complex signal, such that:

[0053]

[0054] It can also be expressed as follows:

[0055] r(t)={u x (t),u y (t)}

[0056] Or even in vector form:

[0057]

[0058] Then, step 40 is performed to frequency decompose the binary signal r(t) into spectral elements characterized by its time-frequency pairs (t, f), also called time-frequency units, and this step is performed periodically to obtain a time and frequency decomposition, called time-frequency decomposition s(t, f), such that:

[0059] s(t,f)=spectre t,f (r(τ))

[0060] The time-frequency decomposition step 40 can be performed in various ways. These various embodiments are described below, providing the time-frequency decomposition s or s in a continuous form, in other words in an analog rather than a discrete form. or or A computer-implemented digital implementation includes both time and frequency sampling steps.

[0061] exist Figure 1 In a first embodiment, denoted by 41 in FIG. 8 , the time-frequency decomposition step 40 is performed using a filter bank around each frequency f.

[0062] Therefore, the time-frequency decomposition s(t,f) is expressed as follows:

[0063]

[0064] Among them, h f is the impulse response of a bandpass filter centered at frequency f, F +are all frequencies greater than or equal to 0.

[0065] In a second embodiment 42, the time-frequency decomposition step 40 is performed using a Fourier transform, in particular a short-term single-sided Fourier transform.

[0066] As a standard, the time-frequency decomposition is expressed as:

[0067]

[0068] In practice, more efficient estimators are preferably used based on division into time intervals, by time weighting, averaging over multiple time intervals, and overlap between consecutive intervals. The formula is then:

[0069]

[0070] Among them, for k = [1, p] and Defines a partition into p intervals around a given date t, possibly with overlap. In general, this partitioning does not depend on t and is the same for each unit. The time range of interval k is

[0071] The total time range of the corresponding unit (t,f) is:

[0072]

[0073] dt=dt - +dt +

[0074] Among them, for k = [1, p] Etw k (τ), defining a time-weighted window, e.g. of the Hanning type, for each of these intervals. Typically, w k Independent of k, it is the same for every interval.

[0075] According to the estimated spectral quantities, the following compensation needs to be introduced:

[0076]

[0077] In the specific case, there is no weight corresponding to w k =1, in this case

[0078] In addition, a subset of dates is introduced: T ↓ ={t′ i ,i=[1,m′]}.

[0079] In a third embodiment 43, the time-frequency decomposition step 40 is performed using a Fourier transform, in particular a short-term bilateral Fourier transform, also called a "full spectrum" transform, in other words, for a set of frequencies F taking values ​​from a set of real numbers.

[0080] Therefore, as a standard, the time-frequency decomposition It is expressed as:

[0081]

[0082] Or where it is divided into time blocks:

[0083]

[0084] In a fourth embodiment 44, a Fourier transform, in particular a short-term quaternion Fourier transform, is used to perform the time-frequency decomposition step 40 using unitary imaginary numbers, verifying that 2 =1j 2 =1k 2 =1i.1j.1k=-1.

[0085] Therefore, as a standard, the time-frequency decomposition It is expressed as:

[0086]

[0087] Or where it is divided into time blocks:

[0088]

[0089]

[0090] The expressions for the Fourier transform provided in the above embodiments 41 to 44 form applicable formulas that produce effective estimators, particularly in terms of their formulas, with time weighting, averaging over multiple time intervals, and overlap between consecutive intervals, and their more general expressions can be provided as:

[0091]

[0092] Among them, w i is the time weighting, μ is defined such that 1μ 2 =-1.

[0093] at last,

[0094]

[0095] Applied to w k (above) or p k The index k (below) means that the weights for different intervals can be different.

[0096] Furthermore, other frequency transforms may be used, such as wavelet decomposition.

[0097] A more general statement is:

[0098]

[0099] Even more generally, the time division and weighting can be varied as a function of the time-frequency unit (t,f):

[0100]

[0101] Trajectories are obtained by inverse transformations of the following type:

[0102]

[0103] Among them, the frequency range of the unit (t, f) is df = df + +df - , the time range of the unit (t,f) is dt=dt + +dt - .

[0104] From each spectral element s(t,f), at fixed date t and frequency f, it is possible to derive the equivalent ellipse from the instantaneous orbit. This can be called local in the time and frequency sense, in other words at date t and frequency f.

[0105] Therefore, step 50 is performed to determine the equivalent ellipse of each spectral element. Regardless of the time-frequency decomposition method, the instantaneous orbit can be expressed in the form of a parametric equation, such that for each component x and y, and where and are the instantaneous amplitude and phase:

[0106]

[0107] For a fixed frequency f, the coverage time t allows obtaining a trajectory at this frequency.

[0108] The instantaneous orbit takes the form of an equivalent ellipse. Assuming s x (t,f),s y (t,f)), varies slowly as a function of time, for example during a complete revolution at the frequency f, and in any case for the duration dt of the time interval defining the spectral element.

[0109] In this case, the date t of the spectral element considered can be distinguished from the time τ of evolution in this spectral element. In addition, by introducing the frequency f into the expression of the phase assumed to be quasi-linear, an equivalent ellipse is obtained in the form of a time-parametric equation for each component x and y:

[0110]

[0111] These parametric equations can also be written as follows, for example:

[0112]

[0113] To obtain these parametric equations, especially in the case of frequency decomposition using filter banks, the parameters a of the equivalent ellipse x (t,f), a y (t,f), can be obtained by estimation, for example direct or quadratic averaging or by RMS value, from - ,t+dt + ] is obtained by taking the instantaneous quantity (τ,f) of .

[0114] In case of frequency decomposition using Fourier transform, the parametric equation of the equivalent ellipse is obtained using the inverse Fourier transform of the frequency elements:

[0115]

[0116] By forming the relevant complex In other words, the binary representation can highlight the decomposition of the parametric equations of two equivalent ellipses in two circles in opposite directions:

[0117]

[0118] After calculation step 59 the following parameters are obtained:

[0119]

[0120] The characterization of the equivalent ellipse is straightforward using the bilateral ("full spectrum") Fourier transform, which can be written directly in polar form:

[0121]

[0122] In general, the equivalent ellipse can be determined and drawn by obtaining its Euler parameters.

[0123] Figure 2 The ellipse and its Euler parameters a(t,f),θ(t,f),χ(t,f), are shown. , these parameters completely define the equivalent ellipse, where:

[0124] a≥0

[0125] θ∈[-π / 2,π / 2]

[0126] χ∈[-π / 4,π / 4]

[0127]

[0128] Furthermore, b is the semi-major axis, i.e., the major radius, and c is the semi-minor axis, i.e., the minor radius, and their signs provide the direction of rotation of the equivalent ellipse.

[0129] The parametric equations for the equivalent elliptical locus are more useful in complex form because:

[0130] -The equation of a circle is specifically expressed as cosine and sin in phase;

[0131] - the axes are expanded to obtain an ellipse;

[0132] -Apply a rotation to it so that it gets the desired orientation, thus:

[0133]

[0134] The direction is understood to be the angle θ of the equivalent ellipse between the major axis and the x-axis. The orientation is understood to describe the direction of rotation of the trajectory of the ellipse.

[0135] This representation of the equivalent ellipse is natural, with a time-frequency decomposition using the Fourier transform of the quaternion, which can be directly converted into the Euler form:

[0136]

[0137] When the inverse Fourier transform is applied to the frequency elements to obtain the time parametric equation of the equivalent elliptical trajectory, the parametric equation has the property of rejecting the single exponential term e 1j.2.π.f.τ Special advantages of the time parameterization:

[0138]

[0139] in, It is plural C 1i Projection of the set.

[0140] More specifically, the step 50 of determining an equivalent ellipse comprises the step of calculating the Euler parameters of the equivalent ellipse.

[0141] Starting from the time-frequency decomposition using a filter bank, we obtain the computation a x and a y Step 51, such that:

[0142]

[0143] Among them, T ↓ is a subset of T.

[0144] Starting from the time-frequency decomposition using a short-term one-sided Fourier transform, we obtain the calculation a x ,a y , and Step 52, such that:

[0145]

[0146] Starting from the time-frequency decomposition using the short-term bilateral Fourier transform, we obtain the calculation a + ,a - ,θ + and θ - Step 53, such that:

[0147]

[0148] The additional calculation step 54 or 55 results in the following Euler parameters:

[0149]

[0150] An inverse calculation of step 56 is also possible, such that:

[0151]

[0152] The method optionally comprises the step of calculating the spectral density of the time-frequency decomposition 60. The spectral density of each component and the cross-spectral density between components are used to estimate the energy distribution between the x and y components.

[0153] Starting from the time-frequency decomposition using a filter bank, a step 61 of calculating the spectral density S is obtained such that:

[0154]

[0155] Starting from the time-frequency decomposition using a short-term one-sided Fourier transform, the spectral density is calculated Step 62, such that:

[0156]

[0157] Starting from the time-frequency decomposition using the short-term bilateral Fourier transform, the spectral density is calculated Step 63, such that:

[0158]

[0159] The following will also be used:

[0160]

[0161] Starting from the time-frequency decomposition using the short-term quaternion Fourier transform, the spectral density is calculated Step 64, such that:

[0162]

[0163] Based on these spectral densities S, and Step 70 is executed to calculate Stokes parameters S0, S1, S2 and S3 of at least one equivalent ellipse.

[0164] The Stokes parameters are four real numbers that are commonly used to describe the polarization state of an electromagnetic wave.

[0165] S0 is usually the total intensity of the electromagnetic wave, and in this case, by extension, the total intensity of the binary signal, S0>0.

[0166] S1 and S2 provide the intensity of linear polarization and the polarization direction of the ellipse

[0167] S3 provides the circular polarization intensity |S3|, whose sign provides the direction of rotation.

[0168] The simplified Stokes parameters are also defined:

[0169]

[0170] Starting from the spectral density obtained for the time-frequency decomposition using a filter bank, a step 71 of calculating the Stokes parameters of at least one equivalent ellipse is obtained such that:

[0171]

[0172] Starting from the spectral density obtained for the time-frequency decomposition using a short-term one-sided Fourier transform, a step 72 of calculating the Stokes parameters of at least one equivalent ellipse is obtained, such that:

[0173]

[0174] Starting from the spectral density obtained for the time-frequency decomposition using the short-term bilateral Fourier transform, a step 73 of calculating the Stokes parameters of at least one equivalent ellipse is obtained such that:

[0175]

[0176] Starting from the spectral density obtained for the time-frequency decomposition using the short-term quaternion Fourier transform, a step 74 of calculating the Stokes parameters of at least one equivalent ellipse is obtained, such that:

[0177]

[0178] As an alternative embodiment, the Stokes parameters S1, S2 and S3 are directly calculated by time-frequency decomposition using the quaternion Fourier transform:

[0179]

[0180] Based on these Stokes parameters, step 75 is performed to calculate the polarization rate As well as the simplified Stokes parameters mentioned above, and the intensity S p of the polarization part.

[0181]

[0182] By polarization rate The polarization represented highlights the cyclostationarity of the equivalent ellipse, i.e. the regularity of the trajectory of said ellipse with respect to the rotation period. The polarization reflects the structuring of said trajectory with respect to the defined frequency. Therefore, the polarization ratio can be calculated for each time-frequency unit resulting from the time-frequency decomposition in order to highlight the cyclostationarity of the rotation axis for a given frequency.

[0183] Furthermore, a calculation step 57 may be implemented to calculate the polarization spectral density S p and the simplified Stokes parameters to determine the Euler parameters a, θ and χ:

[0184]

[0185] Provides the fourth Euler parameter of the phase of the trajectory source It can also be derived from the following calculation step 58:

[0186]

[0187] After the step 50 of determining the equivalent ellipse, in particular by calculating the Euler parameters of said equivalent ellipse, a step 80 of extracting at least one characteristic indicator of the rotation axis from the parameters of the equivalent ellipse, such as Euler or Stokes parameters or parameters derived therefrom, is performed.

[0188] Furthermore, the aforementioned steps are optionally performed at least a second time for additional planes that intersect the axis of rotation of the shaft and are different from the plane on which the steps were initially performed. In this embodiment, a step of comparing the characterizing indicators of the planes may therefore be performed.

[0189] For example, at least one characterization indicator includes the aforementioned polarization rate and / or circularity index (related to |χ|), and / or intensity index and / or amplitude index, and / or rotation direction index (related to the sign of χ), and / or direction index (related to θ), and / or synchronization index of equivalent ellipse (related to related).

[0190] Each element indicator contributes to providing practical and useful characteristics of the rotating system, for example high polarization ratio and high circularity may be due to the rotating axis. Distinguishing this part of the signal, while the complementary part is seen as interference, is useful, for example, for identifying the axis (for modeling purposes) or for better controlling it in case the axis is equipped with magnetic bearings.

[0191] Optionally, at least one characterization indicator is normalized, in other words, its value is between -1 and 1 or between 0 and 1.

[0192] Provide a characterization index for a plane, then represent it as A, or compare two planes, then represent it as I.

[0193] When a characterization index is constructed from any characteristic quantity re-evaluated at each time instant t, the characterization index is called standard, denoted by C. When a characterization index is based on the stationarity of a quantity over time (maximum when the change of the variable over time is zero), the characterization index is called stationary, denoted by S.

[0194] Therefore, the polarization index is expressed as:

[0195]

[0196] For a plane, the strength index is:

[0197]

[0198] The normalization function is:

[0199]

[0200] TT and FF represent sets of universal dates and frequencies, and their values ​​are taken from the set of real-valued values ​​R.

[0201] For a plane, the amplitude index is:

[0202]

[0203] For a plane, the sign index is -1 or 1, depending on the sign of χ:

[0204]

[0205] For a plane, the roundness index is:

[0206]

[0207] For a plane, the symbolic stationarity indicator, in other words the direction of rotation, in other words the orientation, is:

[0208]

[0209] The stationarity function is:

[0210]

[0211] For a plane, the roundness stability index is:

[0212]

[0213] For a plane, the directional stationarity index, in other words the geometric tilt of the ellipse is:

[0214]

[0215] For a plane, the synchronous stationarity index is:

[0216]

[0217] For two planes, each parameter or indicator is redefined for the additional plane by denoting these new parameters with a prime symbol (eg, a').

[0218] The amplitude comparison characterization index is:

[0219]

[0220] The symbolic comparison indicator is a Boolean value between 0 and 1, depending on the results of the following tests:

[0221]

[0222] The roundness comparison characterization index is:

[0223]

[0224] The relative error function is:

[0225] reldif(x,y)=ratio * (2.|xy|,|x|+|y|)

[0226] And the division function exceptions are as follows:

[0227]

[0228] The direction comparison characterizes the index, in other words, the geometric tilt of the ellipse is:

[0229]

[0230] The synchronous comparison characterization indicators are:

[0231]

[0232] The indicators of stability and comparative roundness are:

[0233]

[0234] The indicators of stability and comparison direction are:

[0235]

[0236] The indicators of stability and comparative synchronization characteristics are:

[0237]

[0238] Other indicators can be constructed from the quantities constructed in steps 70 and 50.

[0239] Optionally, step 90 is performed to introduce at least one characterizing indicator into the neural network in order to classify said indicator according to the rotation of the axis and to correlate it with the anomalies listed previously. Anomalies similar to the learned basis are then detected.

[0240] Optionally, a step 100 of displaying at least one extracted characterizing indicator is performed so that it can be read by operators and so that they can understand potential anomalies in the rotating shaft.

[0241] A step 110 of displaying an image of the locus of at least one equivalent ellipse may also be performed.

[0242] Figure 3 The steps of the filtering method according to an example of the present invention are schematically shown. In a specific embodiment, the following steps are performed after the step 80 of extracting the characterization index.

[0243] The filtering method aims at filtering at least one signal to be filtered, for example a signal determined based on a measurement representing the movement of a rotating shaft. The method may or may not be performed in real time. The signal may be one of the input signals determined in step 10 and / or one of the components of the input signal determined in step 20 and / or even a binary signal determined in step 30.

[0244] In order to carry out the filtering method, a step 120 of defining at least one characterizing indicator of the rotating shaft is first carried out, the characterizing indicator being obtained from a frequency analysis of the behavior of the rotating shaft.

[0245] In certain embodiments, the characterization indicator is the indicator extracted during step 80 described above.

[0246] Therefore, at least one characterization index includes the aforementioned polarization rate and / or a circularity index of an equivalent ellipse, and / or an intensity index, and / or an amplitude index, and / or a rotation direction index, and / or a direction index, and / or a synchronization index.

[0247] Then, step 130 is performed to determine a filtering template according to at least one characterization index.

[0248] The step 130 of determining the filter template comprises, for example, a step 131 of calculating a mask such that:

[0249]

[0250] Here, combine is a function that takes as input one or more characterization indicators with values ​​in [0.1] or [-1.1] and presents as output a real value in [0.1].

[0251] After the step 131 of calculating the mask M, a step 132 of calculating the filter template P and its dual P* is performed, such that:

[0252]

[0253] Where N is a frequency weight with a value in [0,1]. N is a random frequency weight independent of M, similar to traditional frequency filtering. For example, N allows to focus on a frequency band around the shaft velocity.

[0254] In addition, double mask (supplement): M * =1-M

[0255] The advantage of considering M* and then P* is that, depending on the application, one can focus on a certain part of the signal obtained according to the characterization metric used, provided by M and / or the residual equivalent to the disturbance provided by M*. For example, one can envision a magnetic bearing controller that reacts differently to rotating parts and external disturbances.

[0256] In one embodiment, the mask M is defined relative to a predefined threshold of a characterization indicator, such as a predefined threshold of polarization rate, and / or a circularity indicator of an equivalent ellipse as described above, and the filter template P is defined by extension.

[0257] The constancy of the characterization indicator can also be used to define a filter template relative to the characterization indicator.

[0258] Finally, step 140 is performed to apply the filter template P to the signal to be filtered, for example a signal determined based on a measurement representing the movement of the rotating shaft.

[0259] In one embodiment, the filter template is applied to the time-frequency decomposition of the binary signal in order to obtain the filtered binary signal R and its jointly computed dual R*. Step 140 is then performed according to various embodiments.

[0260] Starting from the time-frequency decomposition using a short-term one-sided Fourier transform, a binary signal is obtained to calculate the median filter Its dual and the component of the filtered input signal determined in step 20 and Step 141.

[0261]

[0262] and

[0263]

[0264] Starting from the time-frequency decomposition using the short-term bilateral Fourier transform, the binary signal with intermediate filtering is obtained. and its dual Step 142, such that:

[0265]

[0266] Starting from the time-frequency decomposition using the short-term quaternion Fourier transform, we obtain a binary signal for computing the median filter. and its dual Step 143, such that:

[0267]

[0268] Finally, by reconstructing the complete time axis into multiple parts, the following equation 144 can be used to determine the filtered binary signal R and its dual R*:

[0269]

[0270] Optionally, step 150 is performed to obtain filtered input signals U1 to U by projecting the filtered binary signal R onto an axis that is collinear with the measured quantity. M .

[0271] Filter templates allow specific frequency ranges to be selected from the input signal.

[0272] In certain embodiments, multiple filter templates are applied consecutively and / or in combination.Furthermore, the filtering method can be applied to measurements made in different planes or for measurements of different quantities.

[0273] In a particular embodiment, all steps of the method are computer-implemented, with the possibility of being performed in real time, in particular in a magnetic bearing control cabinet.

[0274] Some of the terms and functions used in the above calculations are redefined as follows:

[0275] The set of strictly positive frequencies is:

[0276] The set of strictly negative frequencies is:

[0277] The following are also defined:

[0278] The following are also defined:

[0279] The complete set of frequencies is:

[0280] The general stationarity function is:

[0281]

[0282] The biggest function with exceptions is:

[0283]

[0284] The normalization function is:

[0285]

[0286] The exceptions to this are the division functions:

[0287]

[0288] The relative error function is:

[0289] reldif(x,y)=ratio * (2.|xy|,|x|+|y|)

[0290] The definition of the arctan2 function is also provided as a reminder, and its formula is equivalent to the argument of the complex number x+1μ.y:

[0291] Arg(x+1χ.y)=arctan2(y,x).

Claims

1. A method for filtering at least one signal to be filtered, wherein the filtering is determined based on a measurement representing the movement of a rotating shaft, characterized in that The method comprises the following steps: - defining at least one characterizing indicator of the rotating shaft, wherein the characterizing indicator is obtained from a frequency analysis of the behavior of the rotating shaft (step 120); - Determine a filtering template according to the characterization index (step 130); and - Applying a filter template to the signal to be filtered (step 140).

2. The method according to claim 1, wherein: The characterization index is obtained from the following steps: a) acquiring at least two input signals within a predetermined time period, said input signals comprising measurements representing the movement of a rotation axis, said measurements being non-collinear with each other (step 10); -b) determining two components of the input signal, said components being orthogonal to each other (step 20); -c) combining the two components into a binary signal (step 30); -d) performing a time-frequency decomposition of the binary signal into spectral elements (step 40); -e) determining the equivalent ellipse for each spectral element (step 50); and -f) extracting the characterization index of the rotation axis based on the parameters of the equivalent ellipse (step 80).

3. The method according to claim 2, wherein: The filter template is applied to the time-frequency decomposition of the binary signal to obtain a filtered binary signal.

4. The method according to claim 3, wherein: The time-frequency decomposition of the binary signal to which the filter template is applied is a time-frequency decomposition obtained using a Fourier or wavelet transform, or by filtering, or using a quaternion Fourier transform.

5. The method according to any one of claims 3 and 4, further comprising the step (150) of obtaining a filtered input signal by projecting the filtered binary signal onto an axis collinear with the measured quantity.

6. The method according to any one of claims 3 to 5, further comprising the step of calculating a dual signal of the filtered binary signal.

7. The method according to any one of claims 2 to 6, wherein: The at least one indicator comprises polarization rate, and / or circularity of the equivalent ellipse and / or amplitude and / or direction and / or orientation and / or synchronization indicators.

8. The method according to any one of claims 2 to 7, wherein: The filter template is defined relative to a predefined threshold of polarization rate and / or a circularity index of an equivalent ellipse.

9. The method according to any one of claims 1 to 8, wherein: The filter template is defined based on at least one normalization index ranging between -1 and 1 or between 0 and 1.

10. The method according to any one of claims 1 to 9, wherein: The filter template is a linear binary filter and / or is obtained by multiplying (step 131 ) a mask determined as a function of a characterizing indicator and a frequency weighting.

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